A Framework of Adaptive Multiscale Wavelet Decomposition for Signals on Undirected Graphs

You are here

Top Reasons to Join SPS Today!

1. IEEE Signal Processing Magazine
2. Signal Processing Digital Library*
3. Inside Signal Processing Newsletter
4. SPS Resource Center
5. Career advancement & recognition
6. Discounts on conferences and publications
7. Professional networking
8. Communities for students, young professionals, and women
9. Volunteer opportunities
10. Coming soon! PDH/CEU credits
Click here to learn more.

A Framework of Adaptive Multiscale Wavelet Decomposition for Signals on Undirected Graphs

The state-of-the-art graph wavelet decomposition was constructed by maximum spanning tree (MST)-based downsampling and two-channel graph wavelet filter banks. In this work, we first show that: 1) the existing MST-based downsampling could become unbalanced, i.e., the sampling rate is far from 1/2, which eventually leads to low representation efficiency of the wavelet decomposition; and 2) not only low-pass components, but also some high-pass ones can be decomposed to potentially achieve better decomposition performance. Based on these observations, we propose a new framework of adaptive multiscale graph wavelet decomposition for signals defined on undirected graphs. Specifically, our framework consists of two phases. Phase 1, called pre-processing, addresses the downsampling unbalance issues. We design maximal decomposition level estimation, unbalance detection, and unbalance reduction algorithms such that the downsampling rates of all levels are close to 1/2. Phase 2 concerns about adaptively finding low- or high-pass components that are worthy to be decomposed to improve the compactness of the decomposition. We suggest a graph signal Shannon-entropy-based adaptive decomposition algorithm. With applications on synthetic and real-world graph signals, we demonstrate that our framework provides better performance in terms of downsampling balance and signal compression, compared with other graph wavelet decomposition methods.

SPS on Twitter

SPS Videos

Signal Processing in Home Assistants


Multimedia Forensics

Careers in Signal Processing             


Under the Radar